We investigate the closure properties of read-once oblivious Algebraic Branching Programs (roABPs) under various natural algebraic operations and prove the following.
- Non-closure under factoring: There is a sequence of explicit polynomials $(f_n(x_1,\ldots, x_n))_n$ that have poly(n)-sized roABPs such that some irreducible factor of $f_n$ does not have roABPs ... more >>>